gegenbauer

kyosu::gegenbauer = eve::functor<gegenbauer_t>

inlineconstexpr

Computes the value of the Gegenbauer function of order \(n\).

Computes the value of the Gegenbauer function of order \(n\) and parameter \(\lambda\), \(C^{(\lambda)}_n(z)\) at z. If \(n\) is an integer, the function is a polynomial of degree \(n\).

Header file

#include <kyosu/functions.hpp>

Callable Signatures

namespace eve
{
   // Regular overload
   auto constexpr gegenbauer( auto n, auto lambda, auto z)                          noexcept; // 1
 
   // Lanes masking
   constexpr auto gegenbauer[conditional_expr auto c](/* any previous overload */)  noexcept; // 2
   constexpr auto gegenbauer[logical_value auto m](/* any previous overload */)     noexcept; // 2
}

Parameters

• n, lambda, z : real or cayley_dickson.

Return value

1.The value of the function at z is returned. real input z is treated as complex(z).

1. The operation is performed conditionnaly.

External references

• Wolfram MathWorld: GegenbauerC
• Wikipedia: Gegenbauer polynomials
• DLMF: Gegenbauer Function

Example